MATLAB中NaN与Inf的区别解析：为何不同操作会输出不同结果？

Great question! Let’s break down the differences between Inf and NaN in MATLAB clearly, and walk through why each pops up in specific operations.

These two values serve entirely distinct purposes in MATLAB’s numerical system:

• Inf (Infinity)
  This represents a mathematically defined infinite value—think of it as the limit of a number growing without bound. It has a clear directional meaning (positive or negative) and behaves predictably in many operations. For example, adding a finite number to Inf still gives Inf, and dividing a finite number by Inf gives 0.
• NaN (Not a Number)
  This marks an undefined or indeterminate numerical result. It’s MATLAB’s way of saying "this operation has no valid mathematical answer in the real number system". A key quirk of NaN is that any operation involving it will also return NaN—you can’t "fix" a NaN by combining it with valid numbers.

Let’s look at common scenarios for each:

Operations that return Inf #

• Dividing a non-zero number by 0:

  5 / 0   % Returns Inf
  -7 / 0  % Returns -Inf
  

• Exceeding the maximum value of MATLAB’s double-precision floating point format (≈1.7977e308):

  1e309  % Returns Inf
  

• Calculating logarithms of values approaching 0 (from the positive side):

  log(0)  % Returns -Inf
  

Operations that return NaN #

• Indeterminate forms with no single valid answer:

  0 / 0         % NaN (0 divided by 0 is undefined)
  Inf - Inf     % NaN (∞-∞ can be any value, depending on context)
  Inf * 0       % NaN (∞*0 is also indeterminate)
  

• Operations that have no real-number solution:

  sqrt(-9)  % NaN (square root of negative number is not real)
  log(-3)   % NaN (logarithm of negative number is not real)
  

• Any operation involving NaN itself:

  NaN + 10  % NaN
  NaN * 5   % NaN
  

To sum it up: Inf is for values that are infinitely large/small but mathematically meaningful in a limit sense, while NaN is for results that are completely undefined or have no valid numerical answer.

内容的提问来源于stack exchange，提问作者user10799430